Trespassing on Einstein's Lawn (49 page)

Physicists, Polchinski continued, had studied T-duality in theories with closed strings, but no one had bothered with open strings. “I had grad students,” he said, “and grad students need problems to do. So I said, why not try the same thing with open strings and see what happens? As with all good problems for students, they couldn't figure it out on their own, but we figured it out together. What we found was that the same sort of thing happens: the box gets smaller and smaller, and then past a certain point it grows bigger and bigger. But the funny thing is, when the box gets bigger, it's no longer empty. There's something in it. A submanifold. A brane.”

Unlike closed strings, open strings don't have a winding number. Even if they wrap themselves around a compact dimension, their ends can still move around freely, so they don't create the same kind of tension. In fact, their ends
have
to move around freely. In order to preserve the Poincaré invariance of spacetime—in order to avoid choosing a preferred frame and violating relativity—the strings' endpoints have to be allowed to end at any point in spacetime, a democratic principle known as a Neumann boundary condition.

Without winding numbers, energy for open strings comes only in the form of vibrations—which means that if you shrink the size of one
compact dimension down to zero, it never turns around and grows bigger again. It simply blinks out of existence, leaving the open strings in a spacetime with one less dimension than they started with.

That doesn't sound like a problem, until you remember that any theory with open strings inevitably contains closed strings, too. And with closed strings in the picture, things get a little weird.

Shrink the size of the compact dimension down to zero, and as far as the closed strings are concerned it grows big again, maintaining the full dimensionality of the original spacetime. Meanwhile, from the perspective of the open strings, spacetime loses a dimension.

How could there be a single spacetime that appears to have nine spatial dimensions to the closed strings but only eight to the open ones? Actually, the problem was even more subtle than that, because the majority of an open string is physically identical to a closed string. Only its endpoints are different. So the question, really, was how there could be a single spacetime that appears to have nine spatial dimensions according to both the closed strings and the open strings
except
for the open strings' endpoints, which only see eight.

Remarkably, Polchinski and his grad students solved the puzzle: when the shrinking compact dimension begins growing larger again, the freely moving open strings suddenly find their endpoints stuck to an eight-dimensional submanifold within the full nine-dimensional space. That way, the endpoints experience eight dimensions, while the rest of the open strings and the closed strings all enjoy the full nine. In other words, when the new spacetime emerges from the shrinking dimension, the open strings' boundary conditions change. A Neumann boundary condition is swapped for a Dirichlet one; instead of being free to end at any spacetime point, the strings are nailed to fixed points.

Only that couldn't be the end of the story—because the whole reason for the Neumann boundary condition was to preserve the Poincaré symmetry of spacetime. Dirichlet boundary conditions commit the forbidden crime against relativity: they treat certain reference frames differently than others, choosing a preferred surface in space. You'd think the whole exercise was shot. There was no point in trying to preserve the integrity of spacetime for open strings if you were just going to throw out relativity in the process.

But, again, Polchinski saw the solution: treat the spatial submanifold to which the strings' endpoints are nailed as a dynamic object. An object that can
move.

If the spatial surface can move freely throughout the full nine-dimensional space, carrying the endpoints of the open strings with it, then the democracy of reference frames remains intact, Poincaré symmetry is restored, T-duality holds for open strings, and open and closed strings can happily coexist in the same universe.

It was a pretty amazing creative leap. What looked from one perspective like empty
space
looked from another like an
object.
It was like that image where you see two faces in profile and then suddenly you see that what looked like empty space between them is actually an object, a vase. Polchinski saw that what appeared to be the background space between strings could also be a vase. Given that the entire goal of quantum gravity was to unify spacetime with the objects it contains, it was a pretty big deal. And because it was a kind of membrane born of Dirichlet boundary conditions, he called it a D-brane.

“The D-brane was an object in its own right,” Polchinski told us. “It could move, oscillate, break. That was totally unexpected.” And it didn't have to be eight-dimensional. It could have any number of dimensions.

You can also stack several D-branes together. “When you put a lot of D-branes on top of each other,” Polchinski said, “they'll start to warp space and eventually they'll form a black brane—a black hole that's extended in more dimensions.”

In fact, it was by comparing the background-space perspective and the vase perspective at a black brane that Maldacena first discovered AdS/CFT: the idea that took down any last shred of invariance among strings, particles, and dimensions, the idea that demonstrated exactly how the holographic principle works.

“Maldacena's duality showed that gauge theory, which we thought we understood really well, and string theory, which we didn't understand very well at all, are really the same theory,” Polchinski said. “That's tremendously striking. It's the deepest thing we know about gravity.”

Deepest thing we know about gravity
, I scribbled.
That it emerges as a holographic projection. That it's an illusion. That it's not real.

“Does that mean that quantum physics and spacetime are two ways of looking at the same thing?” I asked.

“Well, there's a tension between the two, and holography means that quantum mechanics wins,” he said. “The quantum framework survives unmodified. What changes is the nature of spacetime.”

“Because it's no longer invariant?”

“That's right,” Polchinski said. “Spacetime is no longer fundamental.”

Polchinski's discovery of D-branes not only led to AdS/CFT, it also fueled the so-called second superstring revolution. The first revolution occurred back when Schwarz and Green realized that string theory was a theory of quantum gravity. It was a major leap forward—until they found themselves burdened with five theories of quantum gravity, waiting for another revolution.

The second revolution kicked off in 1995 when Ed Witten suggested that all five string theories might be different aspects of a single theory, which he dubbed M-theory. But it wasn't until Polchinski discovered D-branes that he could prove it.

With D-branes in hand, Witten was able to show that all five string theories were just different ways of looking at a single theory, M-theory. Actually, to make that work, he had to include one more theory in the mix, only it wasn't a string theory at all. It was a theory known as supergravity.

Supergravity is the theory you get when you make supersymmetry into a local, rather than global, symmetry. I had already seen how that worked with the gauge symmetries: view a wavefunction from a slightly different perspective and you shift its phase, but because the speed of light is finite, you can't shift it throughout the entire wavefunction at once; you can shift it only in one local region. That creates a misalignment of the phase—a misalignment we call a force.

Supersymmetry is the symmetry that allows you to shift your perspective in a way that swaps fermions and bosons, but once again the speed of light prohibits you from doing so everywhere throughout space at once. That means that while fermions and bosons are swapped within your reference frame, they might not be in another—a misalignment that once again requires a force to patch up the differences.
What force is capable of repairing supersymmetry? Intriguingly, gravity. Only in this case, the graviton requires its own supersymmetric partner, the gravitino. Together, the graviton and gravitino constitute a new force: supergravity.

Just as gravity accounts for the mismatches between accelerated and inertial observers—
to turn a curve into a line you have to bend the paper
—supergravity accounts for the fact that what looks like a fermion to one observer looks like a boson to another.

With Polchinski's D-branes, Witten could finally show that all five of the ten-dimensional string theories plus eleven-dimensional supergravity were different aspects of the unified M-theory, related to one another by dualities such as T-duality and S-duality, which mapped high energies in one string theory to low energies in another. That meant that you could start in any one of the six theories and, using dualities, find your way to any other one. If you start with eleven-dimensional supergravity and compactify one of the dimensions to a circle, you get Type IIA string theory; compactify that dimension to a line segment and you get SO(32). Turn up the energy of SO(32) and you'll find yourself in the low-energy regime of Type I string theory; apply T-duality to SO(32) and you're in E
₈
×E
₈
. Turn up the energy of E
₈
×E
₈
and an extra dimension of spacetime emerges, landing you right back in eleven-dimensional supergravity.

It was clear that D-branes were powerful objects. But were they ultimately real? I had my suspicions. D-branes were
made
of spacetime, and Polchinski had said that spacetime wasn't fundamental.

“Are D-branes fundamental?” I asked.

“D-branes are still not the final answer,” he said, “but in some ways they are closer to the final answer than strings themselves. Strings were the wrong starting point. The holographic principle is much closer to the right starting point. String theory …” He paused. “I don't want to say it has withered away, but …”

I laughed. “But it's withered away?”

“You have black holes and you have a quark-gluon plasma, and you can use either one to understand the other,” Polchinski said. “And you never have to mention strings. Strings aren't on either side of that duality, but they provide the logical connection that turns one into the
other. The theory is no longer string theory. Strings are just one classical limit. We're looking for the whole thing.”

“M-theory?” I asked.

“That's right.”

“So it wouldn't be correct to think that the world is ‘made of strings.' ”

“Not at all.”

In fact, I realized, it was starting to look like it wouldn't be correct to say that the world was made of
anything.
In each of the five string theories, the elementary strings, which are supposed to be the most fundamental ingredients of reality, all give rise to different sets of particles. You'd think that would be enough to show that the five theories weren't really the same after all—but you'd be missing half the picture. If for each string theory you list all the elementary particles
and
all the composite particles—particles made out of multiple strings—the lists suddenly appear identical. What's elementary in one theory is composite in another—and yet, thanks to all those dualities, all five theories are equally true.

It was a powerful blow to the whole reductionist enterprise, the one that for centuries had scientists thinking that if they could just find the smallest objects out of which everything else was made, they'd understand the workings of the world. It was also a powerful blow to anyone who happened to be driving down the California coast with her father in search of ultimate reality. String theory was stating it pretty clearly: there are no basic ingredients. They only appear basic depending on your perspective.

“In Maldacena's duality, the strings emerge as composite states of gluons,” Polchinski said. “And in matrix theory, which is another approach to M-theory, you have enormous matrices that reconstruct an eleven-dimensional spacetime and there are no strings anywhere. String theory was a way of getting to the holographic principle. That's really the fundamental thing.”

“But M-theory must have some ontology, right?” I asked. “Can you guess what it might be? Are there strings, branes, particles? Some totally new object? Is there space? Time?”

“I can't even guess,” Polchinski said. “It's remarkable to know so
much about many limits and yet have no good idea of what they are limits of! Holography is clearly part of the answer. The fundamental variables are probably very nonlocal, with local objects emerging dynamically.”

Is it possible that there is no ontology at all? I wondered. Is it a theory made of nothing? Then again, if it's really a theory of everything, wouldn't it have to be?

“So string theory got us to the holographic principle, to AdS/CFT,” I said. “How can we now apply it to our de Sitter universe?”

“Anti–de Sitter space is a pretty special space,” he said. “It's like putting gravity in a box. But the problem that many of us keep coming back to is that we don't live in a box. There are no walls to our universe. So that's the question that needs to be answered.”